And this is without getting into Dyson spheres and other efficient but detectable technology.
Yes, of course. And the heat of a star will make that heat completely invisible in comparison.
The "spectra" that heat would be vented at is infrared, which is infrared no matter the source.
Say you had some gargantuan fusion power harnessing space station in deep space. lots of assumptions here about alien cultures, but this is likely the easiest to detect. They will do whatever they do with their energy, and then vent the waste heat. That heat will be infrared. What does a dim infrared source look like (if even visible at all)? It looks like a brown dwarf. But this is assuming a lot. It assumes some alien would even build brown dwarf sized space stations. We don't know if or even why they would do that.
How do we know this? Because astronomers see these every single night and have developed sophisticated filters to remove them. But by checking how the source is moving it is quite easy to tell if source is local or not, and sure enough all these artificial sources come from satellites, the troposphere, or an unshielded microwave.
It is actually remarkably difficult and a challenging problem in itself to create a communication mechanism which looks like a natural source. It defies imagination to think that every single intelligent species out there has purposefully masked their existence in such a way, including giving up useful technology like ground control radar or mobile communications.
Just think about it. The signals are going to be so weak by the time the photons get here they will be indistinguishable from the CMB.
Any space habitat of any plausible size will be completely undetectable, or at least indistinguishable from a planet. And I would think they'd be much smaller than that.
And structured radio? Lots of possible reasons not to see it. One, possibly not using radio. Two, encryption. Communication will likely look like noise. But even so, the distances involved means long range transmissions will need to be very directed and narrow beam. And even then, it's only a few light years before the signal is undetectable. I would suspect any really long distance communication would be bounced through relays. Also, why? You have to wait years for messages to go around. All of this means no, we're not likely to easily find stray radio signals.